High school learners’ mental construction during solving optimisation problems in Calculus: a South African case study

Brijlall, Deonarain; Ndlovu, Zanele

doi:10.15700/saje.v33n2a679

Cited by 24 publications

(20 citation statements)

References 11 publications

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“…This happens because prospective teachers do not have a good understanding of mathematical concepts. This is in line with the results of research Brijlall & Ndlovu that students can answer derivative questions, but students do not have a good understanding of mathematical concepts to make conceptual mistakes [13].…”

Section: Discussion Of Researchsupporting

confidence: 88%

Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory

Susandi¹,

Sa’dijah²,

As’ari³

et al. 2018

Proceedings of the 1st Annual International Conference on Mathematics, Science, and Education (ICoMSE 2017)

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Mathematical critical thinking is an essential ability for prospective teachers. The prospective teachers must be able to use the ability to think critically well so that students who are taught can also have good mathematical critical thinking skills. However, sometimes prospective teachers have a mistake in solving the problem of critical mathematical thinking skills. The present paper aims to analyze the mistakes of prospective teachers in solving the problem of critical mathematical thinking skills. The type of research method is descriptive with the qualitative approach. The subject in this research is one student of semester VI. The methods used in this research include test method amounting to one essay question, interview method, and triangulation method. The findings show that the prospective teacher on the focus indicator can be completed well whereas the indicators of reason, inference, situation, clarity, and overview, the teacher cannot solve well. Causes of the teacher error based on APOS theory are (1) error in distinguishing between commutative and addition characteristic of multiplication on matrix, (2) error in multiplication operation on the matrix, (3) error inequality of two matrices, and (4) error in the concept of inverse equation matrix.

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Section: Discussion Of Researchsupporting

confidence: 88%

Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory

Susandi¹,

Sa’dijah²,

As’ari³

et al. 2018

Proceedings of the 1st Annual International Conference on Mathematics, Science, and Education (ICoMSE 2017)

View full text Add to dashboard Cite

show abstract

“…This study also supports the conclusion reached by other scholars (e.g., see Brijlall & Ndlovu, 2013;Ledesma, 2011) that the source of difficulties with optimization problems might not necessarily be rooted in the mathematization of the processes but in the difficulty of understanding the underlying mathematical principle. The ultimate extension of this study would be to investigate whether the lab experience helped students with formulating the solution processes to solve textbook problems on optimization.…”

Section: Discussionsupporting

confidence: 90%

The Effect of Math Modeling on Student’s Emerging Understanding

Sokolowski¹

2015

IAFOR J Educ

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This study investigated the effects of applying mathematical modeling on revising students' preconception of the process of optimizing area enclosed by a string of a fixed length. A group of 28 high school pre-calculus students were immersed in modeling activity that included direct measurements, data collecting, and formulating algebraic representation for the data. The lab conduct was enriched by scientific inquiry elements such as hypothesis stating and its verification. While 86% of the students (N=24) falsely hypothesized that the rectangular areas enclosed by a string of a fixed length will remain constant before engaging in the lab, the subsequent tasks of the modeling activity prompted the students to correct their ways of thinking. The study showed that the modeling processes provide ample means of revising students' perception to establish firm conceptual background for inducing a more rigorous algebraic approach to solving problems in math classes. Suggestions for further studies follow.

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“…Action is based on rules and algorithms, where a rule is practised repeatedly until it becomes routine; and this takes place without adequate thinking (Brijlall & Ndlovu, 2013). In the case of trigonometric functions, an individual needs to know the concept of a function first and be able to distinguish trigonometric functions from other functions, such as algebraic, exponential and logarithmic functions.…”

Section: Stages Of Apos Theorymentioning

confidence: 99%

Analysis of errors in derivatives of trigonometric functions

Siyepu

2015

IJ STEM Ed

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Background: This article reports on an analysis of errors that were displayed by students who studied mathematics in Chemical Engineering in derivatives of mostly trigonometric functions. The poor performance of these students triggered this study. The researcher (lecturer) works in a mathematics support programme to enhance students' understanding of mathematics. The purpose of this study was to identify errors and their origins when students did calculations in derivatives of trigonometric functions. The participants of this study were a group of thirty students who were registered for Mathematics in a university of technology in Western Cape, South Africa. The researcher used a qualitative case study approach and collected data from students' written work. This study used Dubinsky's (1991) APOS Theory (Actions, Processes, Objects, and Schemas) to classify errors into categories and analyse the data collected.Results: Errors displayed by students were conceptual and procedural; there were also errors of interpretation and linear extrapolation. Conceptual errors showed a failure to grasp the concepts in a problem and a failure to appreciate the relationships in a problem. Procedural errors occurred when students failed to carry out manipulations or algorithms, even if concepts were understood. Interpretation errors occurred when students wrongly interpreted a concept due to over-generalisation of the existing schema. Linear extrapolation errors occurred when students over-generalised the property f(a + b) = f(a) + f(b), which applies only when f is a linear function, to the form f(a * b) = f(a) * f(b), where f is any function and * any operation. The findings revealed that the participants were not familiar with basic operational signs such as addition, subtraction, multiplication and division of trigonometric functions. The participants demonstrated poor ability to simplify once they had completed differentiation. Conclusions: This study recommends the strategy of focusing on elimination of errors to develop students' understanding of derivatives of trigonometric functions. This can be done through learning activities that lead to identification and analyses of students' errors in classroom discussions.

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High school learners’ mental construction during solving optimisation problems in Calculus: a South African case study

Cited by 24 publications

References 11 publications

Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory

Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory

The Effect of Math Modeling on Student’s Emerging Understanding

Analysis of errors in derivatives of trigonometric functions

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